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Numerical simulation of collapsible-tube flows with sinusoidal forced oscillations
1Graduate School of Biomedical Engineering, University of New South Wales, Sydney, Australia.
Bulletin of Mathematical Biology
|November 1, 1996
Summary
This study explores forced oscillations in collapsible-tube flow, revealing complex dynamics like chaos and period-doubling cascades. These findings enhance our understanding of fluid dynamics in such systems.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Biophysics
Background:
- Collapsible-tube flow with self-excited oscillations is well-studied.
- The combined effect of forced and self-excited oscillations is less understood.
- This phenomenon is relevant in physiological contexts.
Purpose of the Study:
- To numerically investigate the response of forced oscillations in collapsible-tube flow.
- To analyze the interaction between forced and self-excited oscillations using modern dynamics methods.
- To characterize the complex dynamics arising from this interaction.
Main Methods:
- Utilized an ordinary differential equation (ODE) model for collapsible-tube flow.
- Applied modern dynamics methods for numerical investigation.
- Analyzed responses using bifurcation diagrams, Poincaré sections, frequency spectra, and Lyapunov exponents.
Main Results:
- Observed a devil's staircase and period-doubling cascades.
- Identified chaos under specific control parameters (forcing frequency and amplitude).
- Characterized strange attractors with thin fractal structures, linked to high damping and low stiffness.
Conclusions:
- Forced oscillations introduce complex nonlinear behaviors into self-excited collapsible-tube flow.
- The system exhibits chaotic dynamics, period-doubling, and fractal structures.
- System properties like damping and stiffness significantly influence the observed dynamics.